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Register a new userThe $sigma K$ coupling in the chiral unitary approach and the isoscalar $bar{K}N$, $bar{K}A$ interaction
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We evaluate the $sigma$ exchange contribution to the $bar{K}Ntobar{K}N$ scattering within a chiral unitary approach. We show that the chiral transition potentials for $pi pi to K bar{K}$ in the $t$-channel lead to a $sigma$ contribution that vanishes in the $bar{K}$ forward direction and, hence, would produce a null $sigma$ exchange contribution to the $K^-$ optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading order chiral Lagrangian gives an I=0 $pipito Kbar{K}$ amplitude proportional to the squared momentum transfer, $q^2$. This finding poses questions on the meaning or the origin of $sigma$ exchange potentials used in relativistic mean field approaches to the $K^-$ nuclear selfenergy. This elementary $sigma$ exchange potential in $bar{K}Ntobar{K}N$ is compared to the Weinberg-Tomozawa term and is found to be smaller than present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data.
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We report on self-consistent calculations of single-K^- nuclear states and multi-Kbar nuclear states in 12C, 16O, 40Ca and 208Pb within the relativistic mean-field (RMF) approach. Gradient terms motivated by the p-wave resonance Sigma(1385) are found to play a secondary role for single-K^- nuclear systems where the mean-field concept is acceptable. Significant contributions from the Kbar N -> pi Lambda conversion mode, and from the nonmesonic Kbar NN -> YN conversion modes which are assumed to follow a rho^2 density dependence, are evaluated for the deep binding-energy range of over 100 MeV where the decay channel Kbar N -> pi Sigma is closed. Altogether we obtain K^- total decay widths of 50-100 MeV for binding energies exceeding 100 MeV in single-K^- nuclei. Multi-Kbar nuclear calculations indicate that the binding energy per Kbar meson saturates upon increasing the number of Kbar mesons embedded in the nuclear medium. The nuclear and Kbar densities increase only moderately and are close to saturation, with no indication of any kaon-condensation precursor.
The real and imaginary parts of the bar K^0 d scattering length are extracted from the bar K^0 d mass spectrum obtained from the reaction pp to d bar K^0 K^+ measured recently at the Cooler Synchrotron COSY at Julich. We extract a new limit on the K^- d scattering length, namely Im a le 1.3 fm and |Re a| le 1.3 fm. The limit for the imaginary part of the K^- d scattering length is supported by data on the total K^- d cross sections.
The $bar{K} + N to K + Xi$ reaction is studied for center-of-momentum energies ranging from threshold to 3 GeV in an effective Lagrangian approach that includes the hyperon $s$- and $u$-channel contributions as well as a phenomenological contact amplitude. The latter accounts for the rescattering term in the scattering equation and possible short-range dynamics not included explicitly in the model. Existing data are well reproduced and three above-the-threshold resonances were found to be required to describe the data, namely, the $Lambda(1890)$, $Sigma(2030)$, and $Sigma(2250)$. For the latter resonance we have assumed the spin-parity of $J^P=5/2^-$ and a mass of 2265 MeV. The $Sigma(2030)$ resonance is crucial in achieving a good reproduction of not only the measured total and differential cross sections, but also the recoil polarization asymmetry. More precise data are required before a more definitive statement can be made about the other two resonances, in particular, about the $Sigma(2250)$ resonance that is introduced to describe a small bump structure observed in the total cross section of $K^- + p to K^+ + Xi^-$. The present analysis also reveals a peculiar behavior of the total cross section data in the threshold energy region in $K^- + p to K^+ + Xi^-$, where the $P$- and $D$-waves dominate instead of the usual $S$-wave. Predictions for the target-recoil asymmetries of the $bar{K} + N to K + Xi$ reaction are also presented.
We study the coupling of the Lambda(1520)= Lambda* resonance to the bar K* vector meson and nucleon. This coupling is not directly measured from the resonance decay, but is expected to be important in hyperon production reactions, in particular for the exotic Theta+ production. We compute the coupling in two different schemes, one in the chiral unitary model where the Lambda* is dominated by the quasibound state of mesons and baryons, and the other in the quark model where the resonance is a p-wave excitation in the three valence quarks. Although it is possible to construct both models such that they reproduce the bar K N and pi Sigma decays, there is a significant difference between the Lambda* bar K* N couplings in the two models. In the chiral unitary model $|g_{Lambda^*bar{K}^* N}| sim 1.5$, while in the quark model $|g_{Lambda^*bar{K}^* N}| sim 10$. The difference of the results stems from the different structure of the Lambda* in both models, and hence, an experimental determination of this coupling would shed light on the nature of the resonance.
Relativistic mean field calculations of multi-$bar{K}$ hypernuclei are performed by adding $K^-$ mesons to particle-stable configurations of nucleons, $Lambda$ and $Xi$ hyperons. For a given hypernuclear core, the calculated $bar{K}$ separation energy $B_{bar{K}}$ saturates with the number of $bar{K}$ mesons for more than roughly 10 mesons, with $B_{bar{K}}$ bounded from above by 200 MeV. The associated baryonic densities saturate at values 2-3 times nuclear-matter density within a small region where the $bar{K}$-meson densities peak, similarly to what was found for multi-$bar{K}$ nuclei. The calculations demonstrate that particle-stable multistrange ${N,Lambda,Xi }$ configurations are stable against strong-interaction
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